Recent content by kala

Homework Statement Show that (S, *) is a group where S is the set of all real numbers except for -1. Define * on S by a*b=a+b+ab The Attempt at a Solution Well I know that i have to follow the axioms to prove this. So I started with G1 which is associativity. This one I got to...

Oh duh... That was stupid... It doesn't have to be. Thanks

According to the book it is suppose to be an isomorphism, the question says it is. I can get it to be one to one and onto, but i am having trouble with it preserving the operations.

Determine whether the given map \varphi is an isomorphism of the first binary structure with the second. < M2(R ), usual multiplication > with <R, usual multiplication> where \varphi(A) is the determinant of matrix A. The determinant of the matrix is ad-bc, so \varphi(A)=ad-bc. For this...

Homework Statement Consider a comet which passes through its aphelion at a distance rmax from the sun. Imagine that, keeping rmax fixed, we somehow make the angular momentum l smaller and smaller though not actually zero; that is we let l\rightarrow0. Use equations c=l2/\gamma\ mu and...

Homework Statement There is a child's toy, which has the shape of a cylinder mounted on top of a hemisphere (the picture the book has looks like a half of a circle with a square on top.). The radius of the hemisphere is R and the CM of the whole toy is at a height h about the floor. (this in...

Homework Statement Write down the Lagrangian for a cylinder mass m, radius R an moment of inertia I, that rolls without slipping straight down an inclined plane which is at an angle a from the horizontal. Use as your generalized coordinate the cylinder's distance x measure down the plane...

1. Homework Statement This is a question in my classical mechanics book, and i am not very good with polar coordinates. I am suppose to fine r, phi, z in terms of x,y,z. Basically I need to derive the cylindrical polar coordinates from the Cartesian coordinates. The question specifically...

never mind i totally got it to work! thank you for all of the help!

they do ask me that, so do i substitute that in now for F(v)

ok, so understand what i was suppose to do, and got it to work, so was there any reason why they told me what the drag force was?

so in the end when i use the chain rule should I end up with the drag force equation? Sorry I am still a little confused.

Homework Statement This is a question in my classical mechanics book, and i am not very good with polar coordinates. I am suppose to fine r, phi, z in terms of x,y,z. Basically I need to derive the cylindrical polar coordinates from the Cartesian coordinates. The question specifically asks...

So even though the drag force = F(v) i don't sub that part in?

Okay, that is what i have done so far, is this right, I have m*v0= -c*v3/2. then i am suppose to differentiate this using the chain rule which my book is calling the v*dv/dx rule to get a separated form m*v*dv/F(x)=dx. But i don't know what to differentiate with respect to, v or x, but my...